The present disclosure relates to a method for designing a pattern for a lithographic pupil filter for use with a photomask and photoresist to optimize image resolution or to provide frequency doubling for any illumination lens, a lithographic system that employs a photolithographic mask designed by the same, and a method of operating a lithographic system that employs a photolithographic mask designed by the same.
A systematic method of designing a lithographic pupil filter for an arbitrary illumination condition is desired in order to optimize the resolution of a specific feature to be printed in the photoresist. Particularly, a systematic method of designing a lithographic pupil filter for an arbitrary illumination condition is designed for the purpose of printing a specific one-dimensional array of line and space features, for the purpose of printing a specific two-dimensional array of contact holes, for the purpose of frequency doubling for a specific one-dimensional array of line and spacer features, and for the purpose of frequency doubling for a specific two-dimensional array of contact holes. As used throughout the present disclosure, a “frequency doubling” refers to reducing the pitch by 50% so as to provide a higher frequency (double frequency) at a Fourier transformed space (spatial frequency space) derived from the physical space. With frequency doubling, the wafer pitch will be half that of the mask pitch for 1D linespace patterns in the third embodiment and will be that of the mask pitch multiplied by the square root of two for 2D contact arrays in the fourth embodiment.